An integrated circuit (xe2x80x9cICxe2x80x9d) is a semiconductor device that includes many electronic components (e.g., transistors, resistors, diodes, etc.). These components are often interconnected to form multiple circuit components (e.g., gates, cells, memory units, arithmetic units, controllers, decoders, etc.) on the IC. The electronic and circuit components of IC""s are jointly referred to below as xe2x80x9ccomponents.xe2x80x9d
An IC also includes multiple layers of metal and/or polysilicon wiring (collectively referred to below as xe2x80x9cmetal layersxe2x80x9d) that interconnect its electronic and circuit components. For instance, many IC""s are currently fabricated with five metal layers. In theory, the wiring on the metal layers can be all-angle wiring (i.e., the wiring can be in any arbitrary direction). Such all-angle wiring is commonly referred to as Euclidean wiring. In practice, however, each metal layer typically has a preferred wiring direction and the preferred direction alternates between successive metal layers. Many IC""s use the Manhattan wiring model, which specifies alternating layers of preferred-direction horizontal and vertical wiring. In this wiring model, the majority of the wires can only make 90xc2x0 turns. However, occasional diagonal jogs are sometimes allowed on the preferred horizontal and vertical layers.
Design engineers design IC""s by transforming circuit description of the IC""s into geometric descriptions, called layouts. To create layouts, design engineers typically use electronic design automation (xe2x80x9cEDAxe2x80x9d) applications. These applications provide sets of computer-based tools for creating, editing, and analyzing IC design layouts.
EDA applications create layouts by using geometric shapes that represent different materials and devices on IC""s. For instance, EDA tools commonly use rectangular lines to represent the wire segments that interconnect the IC components. These tools also represent electronic and circuit IC components as geometric objects with varying shapes and sizes. For the sake of simplifying the discussion, these geometric objects are shown as rectangular blocks in this document.
Also, in this document, the phrase xe2x80x9ccircuit modulexe2x80x9d refers to the geometric representation of an electronic or circuit IC component by an EDA application. EDA applications typically illustrate circuit modules with pins on their sides. These pins connect to the interconnect lines.
A net is typically defined as a collection of pins that need to be electrically connected. A list of all or some of the nets in a layout is referred to as a net list. In other words, a net list specifies a group of nets, which, in turn, specify the interconnections between a set of pins.
FIG. 1 illustrates an example of an IC layout 100. This layout includes five circuit modules 105, 110, 115, 120, and 125 with pins 130-160. Four interconnect lines 165-180 connect these modules through their pins. In addition, three nets specify the interconnection between the pins. Specifically, pins 135, 145, and 160 define a three-pin net, while pins 130 and 155, and pins 140 and 150 respectively define two two-pin nets. As shown in FIG. 1, a circuit module (such as 105) can have multiple pins on multiple nets.
The IC design process entails various operations. Some of the physical-design operations that EDA applications commonly perform to obtain the IC layouts are: (1) circuit partitioning, which partitions a circuit if the circuit is too large for a single chip; (2) floor planning, which finds the alignment and relative orientation of the circuit modules; (3) placement, which determines more precisely the positions of the circuit modules; (4) routing, which completes the interconnects between the circuit modules; (5) compaction, which compresses the layout to decrease the total IC area; and (6) verification, which checks the layout to ensure that it meets design and functional requirements.
Placement is a key operation in the physical design cycle. It is the process of arranging the circuit modules on a layout, in order to achieve certain objectives, such as reducing layout area, wirelength, wire congestion, etc. A poor placement configuration not only can consume a large area, but it also can make routing difficult and result in poor performance.
Numerous EDA placers have been proposed to date. Certain placers are constrained-optimization placers, which (1) use cost-calculating functions to generate placement scores (i.e., placement costs) that quantify the quality of placement configurations, and (2) use optimization algorithms to modify iteratively the placement configurations to improve the placement scores generated by the cost-calculating functions.
A constrained-optimization placer typically receives (1) a list of circuit modules, (2) an initial placement configuration for these modules, and (3) a net list that specifies the interconnections between the modules. The initial placement configuration can be random (i.e., all the modules can be positioned randomly). Alternatively, the initial configuration can be partially or completely specified by a previous physical-design operation, such as the floor planning.
A constrained-optimization placer then uses a cost-calculating function to measure the quality of the initial placement configuration. The cost function generates a metric score that is indicative of the placement quality. Different cost-calculating functions measure different placement metrics. For instance, as further described below, some functions measure wirelength (e.g., measure each net""s minimum spanning tree, Steiner tree, or bounding-box perimeter, etc.), while others measure congestion (e.g., measure number of nets intersected by cut lines).
After calculating the metric cost of the initial placement configuration, a constrained-optimization placer uses an optimization algorithm to modify iteratively the placement configuration to improve the placement score generated by its cost-calculating function. Different optimization techniques modify the placement configuration differently. For instance, at each iteration, some techniques move one circuit module, others swap two modules, and yet others move a number of related modules. Also, at each iteration, some optimization techniques (e.g., KLFM and tabu search algorithms) search for the best move, while others (e.g., simulated annealing and local optimization) select random moves. In addition, some techniques (e.g., simulated annealing) accept moves that make the metric score worse, whereas others (e.g., local optimization) do not.
Five types of constrained-optimization placement techniques are described below.
Some placers use min-cut bipartitioning. This technique uses horizontal and vertical cut lines to partition the IC layout recursively into successive pairs of regions. At each level of the recursion, this technique then moves the circuit modules between the regions at that level, in order to reduce the number of nets intersected by the cut line for that level. By minimizing the net-cut cost at each level of the recursion, these techniques reduce the wire congestion across the cut lines.
FIGS. 2 and 3 illustrate one example of min-cut bipartitioning. FIG. 2 illustrates an IC layout 200 that is partitioned initially in two regions 210 and 215 by a vertical cut line 205. After defining this initial cut line, the min-cut bipartitioning method calculates the number of nets that are intersected by this cut line. This number is indicative of the wire congestion about this cut line. An optimization algorithm (such as KLFM) is then used to modify the initial placement iteratively (i.e., to move the circuit modules iteratively), in order to minimize the net-cut cost across the initial cut line 205.
Once the congestion across the initial cut line is minimized, the min-cut bipartitioning method is applied recursively to the two regions created by the initial cut line, and then it is applied to the resulting regions created by the succeeding cut lines, and so on. FIG. 3 illustrates the IC layout 200 after it has been recursively partitioned by seven cut lines 205 and 220-245.
The semi-perimeter method is another cost-calculating function used by some constrained-optimization techniques. This method quickly generates an estimate of the wirelength cost of a placement. For each net, this method typically (1) finds the smallest bounding-box rectangle that encloses all the net""s pins, and (2) computes half the perimeter of this bounding rectangle.
FIG. 4 illustrates a bounding box 400 for a net that contains pins 135, 145, and 160 of FIG. 1. The computed semi-perimeter value of this box 400 equals the sum of its width 405 and height 410. This computed semi-perimeter value provides a lower bound estimate on the amount of wire required to route a net.
The semi-perimeter method sums the semi-perimeter values of all the bounding rectangles of all the nets to obtain an estimated wirelength cost for a placement configuration. An optimization technique can then be used to modify iteratively the placement configuration to reduce this wirelength cost estimate, and thereby obtain an acceptable placement configuration.
To estimate the wirelength cost of placement configurations, some constrained-optimization placement techniques compute and add the length of the rectilinear minimum spanning tree (xe2x80x9cRMSTxe2x80x9d) for each net. A net""s RMST is typically defined as a tree that connects (i.e., spans) the net""s pins through the shortest Manhattan wiring route that only branches at the pin locations.
More specifically, the RMST for an N-pin net includes (1) N nodes (also called points or vertices) corresponding to the N pins, and (2) Nxe2x88x921 edges that connect its N nodes. In addition, the edges of the RMST are either horizontal or vertical, and these edges start and end at one of the N nodes of the tree. FIG. 5 illustrates a RMST 505 for the net that contains pins 135, 145, and 160 of FIG. 1.
The sum of the length of the RMST for each net provides an estimate of the wirelength cost of a placement. An optimization algorithm can then be used to modify iteratively the placement configuration to minimize this wirelength cost.
Rectilinear Steiner trees are another type of tree structure that constrained-optimization placement techniques generate to estimate the wirelength cost of placement configurations. Rectilinear Steiner trees are similar to RMST""s except that Steiner trees do not restrict branching to only pin locations. In rectilinear Steiner trees, a horizontal or vertical edge can branch from a point on an edge that connects two other net pins.
To construct a Steiner tree for an N-pin net, additional points, called Steiner points, are typically added to the net. If R Steiner points are added to the net, the rectilinear Steiner tree for the N-pin net is the RMST on the N+R points. FIG. 6 illustrates a Steiner tree 605 for the net that contains pins 135, 145, and 160 of FIG. 1. In this example, the Steiner point that has been added is point 610.
Heuristic techniques are often used to select the R Steiner points and construct the Steiner tree, since these problems cannot be solved in polynomial time. A heuristic technique is a clever algorithm that only searches inside a subspace of the total search space for a good rather than the best solution that satisfies all design constraints.
Hence, to get an estimate of the wirelength cost of a placement, some constrained-optimization placement techniques use heuristic approximations to identify rectilinear Steiner trees for the nets. The sum of the length of the heuristic Steiner trees for all the nets provides an estimate of the wirelength cost of a placement. An optimization algorithm can then be used to modify iteratively the placement configuration to minimize this wirelength cost.
Recursive grid partitioning is another technique for calculating the wirelength cost of placement configurations. A recursive-grid-partitioning placer typically uses sets of crossing horizontal and vertical lines to divide an IC layout recursively into several sub-regions. At each recursion level, the placer then uses an optimization algorithm to move the circuit modules between the sub-regions defined at that recursion level, in order to reduce the wirelength cost. After minimizing the wirelength cost at a particular recursion level, the placer recursively partitions that level""s sub-regions that meet certain criteria, in order to optimize further the wirelength cost within those partitioned sub-regions.
FIGS. 7 and 8 illustrate two examples of this technique. In FIG. 7, an IC layout 700 is recursively divided into quadrisections (i.e., into four regions). Under this approach, minimum spanning trees are typically used to estimate the wirelength cost for connecting modules in different quadrisections.
FIG. 8 illustrates recursively dividing an IC layout 800 into nine regions. This style of partitioning is sometimes referred to as xe2x80x9csharpxe2x80x9d partitioning. For this type of partitioning, Steiner trees are typically used to estimate the wirelength cost for connecting modules in different regions.
The above-described placement techniques do not consider diagonal wiring in calculating their placement-configuration cost. Hence, when diagonal routes are selected for the interconnect lines, these techniques result in poor placement configurations, which inefficiently consume the layout area, utilize too much wire, and/or have poor wire congestions. Consequently, there is a need in the art for placers that consider diagonal wiring in calculating their placement-configuration costs.
Some embodiments of the invention use a recursive partitioning method to place circuit elements in an IC layout. This method starts each time it receives the coordinates for a region of the IC layout. The received region can be the entire IC layout, or a portion of this layout. In some embodiments, this method also receives a net list that specifies all the net""s that have circuit elements (e.g., have pins or circuit modules) in the received IC region. In other embodiments, the method receives a list of all the circuit elements (e.g., a list of all pins or circuit modules) in the received IC region, and from this list the method identifies the nets that have circuit elements in the received IC region.
This method initially defines a number of partitioning lines that divide the received IC region into several sub-regions (also called slots). In some embodiments, the partitioning lines are intersecting cut lines that define a partitioning grid. In some of these embodiments, the intersecting partitioning lines are N horizontal and M vertical lines that divide the received IC region into (N+1)(M+1) sub-regions, where N and M can equal any integer.
After defining the partitioning lines, the placement method identifies, for each received or identified net, the set of sub-regions (i.e., the set of slots) that contain the circuit elements (e.g., the pins or circuit modules) of that net. The set of sub-regions for each net represents the net""s configuration with respect to the defined partitioning lines.
Next, for each received or identified net, the placement method identifies attribute or attributes of a connection graph that models the net""s configuration with respect to the partitioning lines. The connection graph for each net provides a topology of interconnect lines that connect the slots that contain the net""s circuit elements. According to some embodiments of the invention, the connection graph for each net can have edges that are completely or partially diagonal.
Different embodiments identify different attributes of a net""s connection graph. The attributes can include the length of the connection graph, the number of bends in the connection graph, the probability of the connection graph intersecting the partitioning lines, etc. Also, some embodiments might just identify one attribute (e.g., length) of each net""s connection graph, while other embodiments might identify several attributes (e.g., length and number of bends) of each net""s connection graph.
In some embodiments, the placement method identifies the attribute or attributes of each net""s connection graph by constructing this connection graph in real-time and quantifying its attribute or attributes during or after the construction of the graph. However, other embodiments identify the attributes of the connection graphs in a different manner. Before the placement method starts, these embodiments (1) construct the connection graphs for each possible net configuration with respect to the partitioning lines, and (2) pre-tabulate the attributes of the connection graphs in memory. Some embodiments might pre-tabulate the multiple attributes of the connection graphs. Also, some embodiments might pre-tabulate attributes of connection graphs that are based on different wiring models. During placement, these pre-tabulating embodiments then retrieve, for each identified net configuration, the attribute or attributes of the connection graph associated with the identified net configuration from memory.
The placement method calculates the cost of the placement layout within the received region from the identified connection-graph attributes. For instance, when the identified attribute is the length of the graphs, some embodiments calculate the cost of a placement configuration within the received IC region, by combining (e.g., summing, multiplying, etc.) the length of the graphs, associated with the net configurations, within the received region. Alternatively, when the identified attributes are the length and bend-count of the graphs, some embodiments calculate the placement cost by generating a weighted sum of the length and bend-count.
Next, the placement method uses an optimization algorithm that iteratively modifies the placement configuration in the received IC regions, in order to improve the placement cost. Different embodiments of the invention use different optimization techniques, such as annealing, local optimization, KLFM, tabu search, etc.
After each iterative modification during optimization, the placement configuration is re-calculated by repeating the cost-calculating operations described above for all the nets or for just the nets on which the moved circuit element or elements reside. After optimizing the placement configuration within a received region, the placement method recursively performs the above-described partitioning and optimization operations on each sub-region defined that meets one or more criteria. For instance, some embodiments recursively perform the partitioning and optimization operations on each sub-region that contains more than a specified number of circuit elements.